ARLINGTON -- Josh Hamilton, who is looking for a long-term contract worth $20-25 million annually, has turned down the Rangers' qualifying offer of $13.3 million.

The offer, made a week ago, was required for the Rangers to get Draft pick compensation if Hamilton signs with another team. The Rangers expected Hamilton to reject the offer but still have interest in re-signing him. The Rangers have stayed in contact with Hamilton's agent, Michael Moye, and expect to have further conversations as the offseason progresses.

No clear favorite has yet to emerge in the pursuit. Teams have been mentioned as having potential interest including the Brewers, Orioles, Mariners and Red Sox. But there may be some reluctance to offer Hamilton a contract longer than 4-5 years because of his age (31) and history of injuries.

The Rangers are likely to be among the teams not wanting to offer an extended long-term deal although nobody has a real feel yet what it will take to sign Hamilton. The Rangers are expecting to make one more run at signing Hamilton before he makes his final decision.

"We know all the possible ways it can play," said general manager Jon Daniels, who is attending the GM Meetings this week. "Josh has intimated that we'd get an option. We'd talk before he does something. I'd expect we'll talk before he does something."

The Rangers aren't sitting around and waiting on Hamilton. They have other needs to address, including bullpen and catcher. They'll try to reinforce their starting rotation by pursuing Zack Greinke. They are also concerned about the loss of offense if Hamilton departs.

The Rangers know they are not going to replace Hamilton's production but they are concerned about finding another left-handed bat. Right now their lineup is heavy from the right side with Adrian Beltre, Nelson Cruz, Michael Young, Ian Kinsler, Elvis Andrus and Geovany Soto. Their best left-handed hitters are David Murphy, Mitch Moreland and Leonys Martin.

"We're going to be pretty right-handed, so if there is an opportunity to pick up a left-handed bat, you have to look at it," club president Nolan Ryan said.

The Rangers have some interest in free agent outfielder B.J. Upton because he can play center field while providing 20-25 home runs, 75-80 RBIs and 35-40 stolen bases a year. But he is also right-handed as is Torii Hunter, who lives in North Texas and has expressed a desire in the past to play for the Rangers.

The Diamondbacks are shopping outfielder Justin Upton. The Rangers have talked to them but aren't interested in satisfying Arizona's demand for a shortstop by giving up Andrus or Jurickson Profar. Upton, like his brother, is also a right-handed hitter.

The best free-agent outfielder who can hit from the left side is Nick Swisher. He is a switch-hitter but also strictly a corner outfielder. The Rangers have lukewarm interest in him.

Michael Bourn is a left-handed hitter who can play center field but the Rangers aren't planning on pursuing him. Bourn is a leadoff hitter and the Rangers have Kinsler and Andrus to hit at the top of the lineup. The Rangers want somebody to hit in the middle of the order.

They have looked beyond just outfielders. The Rangers showed some interest in David Ortiz before he re-signed with the Red Sox. They have also shown some interest in free-agent first baseman Adam LaRoche, 33, who hit .271 with 33 home runs, 100 RBIs and a .510 slugging percentage for the Nationals this past season.